Computed tomography (CT) is a widely used technique to infer the properties of a volume interacting with a signal based on the properties of the signals that are projected through the volume at multiple different angles in one or two dimensions. CT is used with X-ray sources (either fan shaped or cone shaped), or with gamma ray sources in Positron Emission Tomography and Single Photon Emission computed Tomography (SPECT). The property measured is the attenuation of the signal as it traverses the volume of the subject. The values for the property in the inferred volume is distributed in two dimensions as slices (presented as images) or three dimensions as a series of stacked slices.
When the same volume is measured at different times, time provides a fourth dimension; and, the resulting data set is called a four dimensional (4D) data set. When the subject of the 4D CT measurement is a living animal, such as a human patient, motion of the heart and lungs and diaphragm, and tissues adjacent thereto, can confound the determination of the distribution of the property values in the volume.
For example, a concern with the irradiation of lung cancers is that many of these tumors move with respiration. Motion poses a number of special problems, including problems with accurate target definition (moving targets may appear with distorted shapes and in wrong locations on CT) and increased irradiation of normal tissues (larger fields are often used to ensure that the tumor is not missed). To improve the visualization of moving tumors, a variety of techniques have been proposed. One of the simplest is voluntary breath hold, in which the patient holds his or her breath during imaging. This is often problematic, however, in many lung cancer patients due to poor lung function. A more sophisticated approach has been implemented known as 4D computed tomography (4DCT) imaging and respiratory gating. Such periodic motions are often divided into multiple different motion phases, so that within each motion phase the position of values in the volume are relatively stable. A 4D CT scan is composed of a large number of individual CT scans obtained at various phases of the respiratory cycle. This approach allows the radiation oncologist to watch the movement of the tumor with respiration.
Reconstructing good quality images for Four-Dimensional Computed Tomography (4DCT) or Four-Dimensional Cone-Beam Computed Tomography (4D-CBCT) is always challenging especially when the data are under-sampled for each individual phase. For example, CBCT data is often acquired with limited number of projections, so that an individual motion phase may be under-sampled. Thus, while the limited number of projections is sufficient to reconstruct decent motion-averaged images; reconstructing a 4D image from this limited data leads to motion-induced artifacts. Under-sampled projection data from moving objects within a subject are reconstructed using: either a) simple filtered back projection, or b) iterative techniques that minimize or maximize some optimality criteria.
While filtered back projection is computationally efficient, using the technique with under-sampled data often leads to severe reconstruction artifacts. Iterative methods overcome this limitation by reducing the artifacts; however these techniques are computationally complex and often require either advanced reconstruction engines to handle the computational complexity or longer computation time.